152 DYNAMICS OF A RIGID BODY. 



the screw complex As, A if A 5 . Hence / belongs to 

 (A i, A z ), and also to (A 3 , A^ A 6 ). If, therefore, forces 

 along A ly ... A 5 equilibrate, then the forces along 

 A i, A 2 must compound into a wrench on /. This condi- 

 tion determines the forces on A i9 A 2 ( 17). 



141. Problem. A free rigid body is acted upon by 

 five forces : show how to move the body so that it shall 

 not do work against nor receive energy from any one of 

 the forces. 



Let A i, . . . A 5 be the five forces. Draw two trans- 

 versals Z, M intersecting A l9 ... A^. Construct the 

 cylindroid of which Z, Mare the screws of zero pitch; 

 find, upon this cylindroid, the screw X reciprocal to A 5 . 

 Then the only movement which the body can receive, 

 so as to fulfil the prescribed conditions, is a twist about 

 the screw X. For X is then reciprocal to A l9 . . . A 5 , 

 and therefore a body only free to twist about X will be 

 Unacted upon by any forces directed along A^ . . . A 5 . 



From the theory of reciprocal screws it follows that 

 a body rotated around any of the lines A ly . . . A s will 

 not do work against nor receive energy from a wrench 

 on X 



As a particular case, if A ly . . . A 5 have a common 

 transversal, then X is that transversal, and its pitch is 

 zero. In this case it is sufficiently obvious that A ly . . . A 5 

 cannot disturb the equilibrium of a body only free to 

 rotate about X. 



142. Impulsive Screws and Instantaneous Screws. A 

 body which is free to twist about all the screws of a 

 screw complex of the fourth order receives an impulsive 

 wrench on the screw q. It is required to calculate the 

 co-ordinates of the screw about which the body will 

 commence to twist, and also the initial reactions of the 

 constraints. 



Let A and /m be any two screws on the reciprocal 



